Calculating Work for Displacement of Floating Cylinder

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Homework Help Overview

The problem involves calculating the work required to push a floating cylinder deeper into water, specifically a 4 cm diameter cylinder being pushed 10 cm deeper. The context is centered around fluid mechanics and work-energy principles.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the integral approach used to calculate work and question the accuracy of the radius used in the calculations. There are concerns about discrepancies between the calculated answer and the answer provided in the textbook.

Discussion Status

The discussion is ongoing, with participants exploring different interpretations of the problem and questioning the calculations. Some participants express confidence in the original poster's approach, while others are seeking clarification on potential mistakes.

Contextual Notes

There is a sense of urgency as the original poster notes a homework deadline. Additionally, there are concerns about the accuracy of the textbook answer and the possibility of misreading problem data.

bcjochim07
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Homework Statement


A 4 cm diameter cylinder floats in the water. How much work must be done to push the cylinder 10 cm deeper into the water?


Homework Equations





The Attempt at a Solution



I did the integral from 0 to .1 m of (.02m)^2 * pi * (1000kg/m^3) * (9.80) * x dx

= (12.3 x^2)/2 evaluated from 0 to .1 = .0615 J. However, the back of my book says .615 J. Somehow I ended up a decimal place off. Could someone help me?
 
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Anyone have any thoughts on this one?
 
Isn't the radius=0.2 instead of 0.02 ?
 
no, I'm pretty sure the radius is correct

4 cm/2 = radius of 2 cm 2cm * 1m/100cm = .02 m
 
Any thoughts would be greatly appreciated
 
I think that given the values you are working with that your answer is correct.
 
I am concerned because the back of my book says it's .615 J and I can't figure out what's wrong with mine
 
Can somebody find my mistake?
 
I need some help with this one pretty soon because my homework is due tomorrow. Thanks!
 
  • #10
Sometimes the answer in the book is wrong...or the problem data has been misread. In either case it looks like to me that your answer is correct, If not, I would also like to know why and maybe another reader can set us both strait.
 

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